Theorems · Definition · linear algebra

PiTensorProduct.lift

{ι : Type u_1} →
  {R : Type u_4} →
    [inst : CommSemiring R] →
      {s : ι → Type u_7} →
        [inst_1 : (i : ι) → AddCommMonoid (s i)] →
          [inst_2 : (i : ι) → Module R (s i)] →
            {E : Type u_9} →
              [inst_3 : AddCommMonoid E] →
                [inst_4 : Module R E] → MultilinearMap R s E ≃ₗ[R] (PiTensorProduct R fun i => s i) →ₗ[R] E

Constructing a linear map (⨂[R] i, s i) → E given a MultilinearMap R s E with the property that its composition with the canonical MultilinearMap R s E is the given multilinear map φ.

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Basic

Cited by

30 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule